What examples are there of unrelated physical quantities measured in the same units? Torque and energy have the same dimensionality, and so logically are measured in the same units (joules). However, it seems more natural to call the unit for the former a “newton-metre”, because torque does not feel like a form of energy, even though this elaborately described unit means no more or less than a joule.
I could not think of another example of two quantities physically quite different in character that would be measured in the same units, but I expect that there are others. Any examples, please?
 A: The pair of frequency (Hertz) and radioactivity (Becquerel) might fit your requirements. While the former describes a periodic phenomenon, with equal time between events, the latter describes a statistical process, mainly in radioactive decay. Both units translate to one per second.
A: Some other examples include specific heat and specific entropy (J/(K*kg)), angular speed and frequency (or for example specific growth rate) (1/s), and concentration and density (kg/m^3).
Not so coincidentally all of these physical quantities with the same units are closely related to each other and can be converted into the other by the means of some numerical factor or factor with dimensions that cancel out. For example converting from torque to work requires multiple by the angular displacement which has units of m_arclength/m_radius.
A: A few other examples:
Kinematic Viscosity and Diffusion Coefficients both have dimensions of Length$^2$/Time.
Pressure-driven Permeability has dimensions of Length$^2$, the same as area.
There are undoubtedly many more, and I don't think there's any deep underlying message.
A: Time and Specific Impulse are both measured in seconds.
A: Angular momentum and action have the same dimensions, and Planck’s constant quantizes both.
A: There are several unitless quantities:


*

*pure numbers, 

*angles (having cancelled units of m/m), and other nondimensionalized quantities: Fresnel number, numerical aperture, Nusselt number, Reynolds number, and Schmidt number, 

*the fine structure constant, 

*the coupling constant of the strong nuclear force, 

*and a hodge-podge of very niche things: the proton/electron mass ratio, the gravitational coupling constant (gravitational attraction between electrons), ...

A: In Gaussian units in electrodynamics (https://en.wikipedia.org/wiki/Gaussian_units), there are some coincidences:

*

*Capacitance is in $\text{cm}$, just as length

*Resistivity is in $\text{s}$, just as time

*Conductivity is in $\text{cm/s}$, just as velocity

